Characterising Probabilistic Alternating Simulation for Concurrent Games

Probabilistic game structures combine both nondeterminism and stochasticity, where players repeatedly take actions simultaneously to move to the next state of the concurrent game. Probabilistic alternating simulation is an important tool to compare the behaviour of different probabilistic game structures. In this paper, we present a sound and complete modal characterisation of this simulation relation by proposing a new logic based on probability distributions. The logic enables a player to enforce a property in the next state or distribution. Its extension with fixpoints, which also characterises the simulation relation, can express a lot of interesting properties in practical applications.